Abstract

Bose-Einstein condensation where there is a macroscopic occupation of a single low energy state can occur in three dimensional systems. In two dimensions, a transition of this kind is only possible in the presence of a trap. Instead, for two-dimensional homogeneous systems, the Berezinskii-Kosterlitz-Thouless phase transition is expected, in which a phase transition is mediated by the proliferation of topological defects, governs the critical behavior of a wide range of equilibrium two-dimensional systems with a continuous symmetry, ranging from spin systems to superconducting thin films and two-dimensional Bose fluids, such as liquid helium and ultracold atoms. In this thesis, we show that this phenomenon is not restricted to thermal equilibrium, rather it survives more generally in a dissipative highly nonequilibrium system driven into a steady state. By considering a quantum fluid of polaritons of an experimentally relevant size, in the so-called optical parametric oscillator regime, we demonstrate that it indeed undergoes a phase transition associated with a vortex binding-unbinding mechanism. Yet, the exponent of the power-law decay of the first-order correlation function in the (algebraically) ordered phase can exceed the equilibrium upper limit: this shows that the ordered phase of driven-dissipative systems can sustain a higher level of collective excitations before the order is destroyed by topological defects. Our work suggests that the macroscopic coherence phenomena, observed recently in interacting two- dimensional light-matter systems, result from a nonequilibrium phase transition of the Berezinskii- Kosterlitz-Thouless rather than the Bose-Einstein condensation type.